if order of a= order of b in a finite Abelian group , is order of...

if order of a= order of b in a finite Abelian group , is order of ab= order of a?

Expert Solution

If you have any doubts in the solution please ask me in comments...

Given claim is not true if you take abelian group {1,-1,i,-i}

Here we have

order of (i)= order of (-i) =4

But order of (-i×i=1) is =1 which is not equal to 4

Colby Messinger answered 2 years ago

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